Showing papers on "Nonparametric statistics published in 1968"

Pattern Classifier Design by Linear Programming

Abstract: —A common nonparametric method for designing linear discriminant functions for pattern classification is the iterative, or "adaptive," weight adjustment procedure, which designs the discriminant function to do well on a set of typical patterns. This paper presents a linear programming formulation of discriminant function design which minimizes the same objective function as the "fixed-increment" adaptive method. With this formulation, as with the adaptive methods, weights which tend to minimize the number of classification errors are computed for both separable and nonseparable pattern sets, and not just for separable pattern sets as has been the emphasis in previous linear programming formulations.

Nonparametric Discrimination Using Tolerance Regions

Abstract: Nonparametric discrimination among distributions on Euclidean space with continuous distribution functions by tolerance regions method, emphasizing errors probability distribution control

Order Statistics for Discrete Populations and for Grouped Samples

Abstract: The aim of this paper is two-fold: (1) To give a unified treatment of the theory of order statistics when the parent distribution is not necessarily continuous. (2) To assess the effects of grouping on the distribution of order statistics and to indicate the convenience, under suitable conditions, of using order statistics for the estimation of parameters from grouped data with or without censoring.

Certain Uncorrelated Nonparametric Test Statistics

Abstract: It is shown that odd translation invariant two sample statistics are uncorrelated with even translation invariant two sample statistics when the distribution function of the combined sample is equally symmetric. This is a generalization of a result of Hogg. It is used to establish conditions under which certain dispersion test statistics (including ones proposed by Lehmann, Mood, Ansari-Bradley-Freund-Barton-David, Klotz and Moses) are uncorrelated with certain location test statistics (including the Mann-Whitney-Wilcoxon and normal scores).

Nonparametric Ranking Procedures for Comparison with a Control

Abstract: Nonparametric ranking procedures /based on order statistics/ guaranteeing preassigned probability for selection from random samples populations as good as control

On mode estimation in pattern recognition

Abstract: A procedure for determining the modes of a continuous univariate probability density function (pdf) is suggested Inherent in this procedure is the use of a new nonparametric estimate of the pdf An extension of this method to the multidimensional case is posed and some results of the procedure applied to real data problems are presented

Robust estimates of linear trend in multivariate time series

Abstract: Median and weighted median estimates are obtained for the linear trend parameters of a univariate time series by applying the Hodges-Lehmann method to some well known nonparametric tests for trend. The estimation procedure is extended to the multivariate trend model and asymptotic efficiency properties relative to the classical estimates are studied.

An efficient nonparametric detector based on a three-sample classification model

Abstract: The proposed detector uses three vector samples to decide which one of two distinct stationary or quasi-stationary stochastic processes is present at its input. A reference sample is obtained from each of the two processes during an initial learning interval, and the third sample is taken on the decision interval. It is assumed that independent samples can be obtained from the stochastic processes. A weighted linear combination of two 2 -sample Mann-Whitney statistics defined on the three vector samples is used at the detector. An upper bound on the asymptotic or large-sample error probability is obtained, which indicates that, unlike the 2 -sample detector, the new detector is insensitive to the {\em a priori} signal probability and operates well in an unspecified environment. Comparisons are made between the proposed model and the standard 2 -sample model at both small and large values of signal-to-noise ratio. An extension to intermediate values of signal-to-noise ratio is obtained by considering two examples, dc signal in additive noise and Lehmann's nonparametric class of alternatives. Owing mainly to an invariant optimum threshold setting, the proposed procedure results in a significantly better performance over a wide range of signal-to-noise ratio.

Recursive Generation of the Distribution of Several Non-Parametric Test Statistics Under Censoring

Abstract: The exact distributions of several non-parametric test statistics based on (usually) censored samples are obtained recursively under certain non-parametric classes of alternatives.

Multivariate transvariation theory among several distributions and its economic applications.

Abstract: : The report describes the theory of transvariation for multivariate distribution functions. The author has defined and deduced the parameters of transvariation; first, without any assumption of parametric distribution functions (nonparametric case); and second, under the assumption of multivariate normal distributions. The research continued with the study of the theory of transvariation among several (three or more) multivariate distribution functions. For the purpose of simplifying computation, the author has introduced a linear transformation that allows the application of bivariate transvariation theory to the transformed variables. The multivariate normal distribution is considered after the proof of two Lemmas regarding the distribution of a linear function of correlated normal random variables. For the case of more than two multivariate distributions, Gini's aggregative method is applied to simplify further the computations in the applications. The applications of this paper are in the field of comparative static economics. They affirm the fruitfulness of transvariation theory as a quantitative method in comparative statics (intertemporal and interspatial comparative analysis). (Author)

On the Efficacy of Mixed Locally-Most-Powerful One- and Two-Sample Rank Tests (Corresp.)

Abstract: A recent work by the authors describes a new class of nonparametric statistics formed by summing the rank statistics on data subsets of a fixed number of sample values m . This paper derives the locally-most-powerful tests of this class under the assumption of independent sampling.

A non-parametric method for feature selection

Abstract: A non-parametric feature selection technique is proposed It is hoped that a finite number of classes is represented by some finite number of unknown probability structures which are distributed in a finite discrete measurement space No assumptions of statistical independence between pattern measurements will be made The proposed non-parametric feature selection criterion is based on the direct estimation of the minimal expected error rates for a given data set of training samples and is independent from the classification technique used The properties of the proposed feature section are demonstrated using data from agricultural remote sensing

Some Recent Developments In Nonparametric Statistics

Abstract: The main motivation for the development of nonparametric statistics was the need for statistical methods that have desirable properties when little is assumed about the population or populations being sampled. For a number of problems tests were designed whose probability of falsely rejecting the hypothesis was equal or at most equal to a specified constant under little or no assumptions beyond that of random sampling and which were consistent (that is, had error probabilities approaching zero with increasing sample size) in a wide class of alternatives. Classical examples are Smirnov’s two-sample test, which is consistent against all alternatives of the two-sample problem, and Wilcoxon’s two-sample test, whose domain of consistency is more restricted. These two tests depend only on the rank order of the observations and therefore seem to discard much information contained in the sample. It seemed reasonable to expect that a test which is valid under few assumptions, and especially a rank test, could not be nearly as powerful in a parametric class of distributions as an optimal parametric test for that class. It came therefore as a surprise when it was found that often there are nonparametric tests, including rank tests, which compare favorably with corresponding classical parametric tests.

Tabulations of the exact distributions of some renyi-type statistics.

Abstract: : Tables are given of exact distributions for the three Renyi-type statistics. Expressions are given for the limiting and for the exact distributions of these three statistics. Applications of the tables are discussed and examples are given.

Elements of Nonparametric Statistics, Gottfried E. Noether, New York, John Wiley. Pp. X, 104.

Abstract: (1968). Elements of Nonparametric Statistics, Gottfried E. Noether, New York, John Wiley. Pp. X, 104. Journal of the American Statistical Association: Vol. 63, No. 322, pp. 728-728.

Nonparametric detection with dependent observations.

Abstract: Nonparametric detection with dependent observation, discussing asymptotic relative efficiency of Mann-Whitney detector

Study of nonparametric techniques for estimating reliability and other life quality parameters Final report

Abstract: Nonparametric techniques for probability distribution, probability density, and hazard function estimates for life quality